Rotational motion roller coaster problem

In summary, the conversation discusses solving for the normal force and speed of a car on a track using the equations for centripetal force. The correct equations are used for both parts, with a small mistake in part B initially but corrected later. The final answer for part B is v = 12.1 m/s.
  • #1
joe426
44
0

Homework Statement



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Homework Equations


ƩF = ma = (mv2) / r


The Attempt at a Solution



For part A:
Fn - Fg = (mv2) / r
Fn = ((mv2) / r ) + mg
Fn = (500x20^2) / 10 + 500x9.8
Fn = 24900

This seems too high to be true. But I'm unsure of what I did wrong. I know the normal force is the force of which the track is acting on the car.

For part B:
I think it is just 20m/s but I'm not sure. I know an object traveling in a circle has the most speed when it's at the bottom of the circle.

Thanks for the help in advance!
 
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  • #2
Part A looks correct.

For part B, set up equations similar to part A and think about what happens to the value of Fn when the vehicle leaves the track.
 
  • #3
TSny said:
Part A looks correct.

For part B, set up equations similar to part A and think about what happens to the value of Fn when the vehicle leaves the track.

Hmm...

I think Fn would equal 0 when the vehicle leaves the track. So I use the same equation as part A except I set Fn to 0 and solve for v?
 
  • #4
joe426 said:
Hmm...

I think Fn would equal 0 when the vehicle leaves the track. So I use the same equation as part A except I set Fn to 0 and solve for v?

Yes Fn will be zero. Good. But if you use the same equation you will end up taking the square root of a negative number (oops). Set up a correct similar equation using a new free body diagram for point B
 
  • #5
TSny said:
Yes Fn will be zero. Good. But if you use the same equation you will end up taking the square root of a negative number (oops). Set up a correct similar equation using a new free body diagram for point B

Fg - Fn = (mv2) / r
(mgr / m)1/2 = v
(500x9.8x15 / 500)1/2 = 12.1

V = 12.1
 
  • #6
Good! (minus 1 point for not including units :devil:)
 
  • #7
TSny said:
Good! (minus 1 point for not including units :devil:)

Haha thank you so much! I got the units on my paper :P
 

Related to Rotational motion roller coaster problem

1. What is rotational motion in the context of a roller coaster?

Rotational motion refers to the circular movement of an object around a fixed axis or point. In the context of a roller coaster, this refers to the movement of the cars along the track, which is made up of curved sections and loops.

2. How does rotational motion affect the design and construction of a roller coaster?

Rotational motion plays a crucial role in the design and construction of a roller coaster. The track must be carefully designed to ensure that the cars can safely navigate through the curves and loops without losing contact with the track. The size and shape of the loops and curves also impact the speed and forces experienced by the riders.

3. What is centripetal force and how does it relate to rotational motion in a roller coaster?

Centripetal force is the force that keeps an object moving in a circular path. In a roller coaster, this force is provided by the track and is essential for keeping the cars on the track as they move through curves and loops. Without centripetal force, the cars would fly off the track due to their inertia.

4. How do engineers calculate the forces and velocities involved in a roller coaster's rotational motion?

Engineers use mathematical equations, such as Newton's laws of motion and the principles of conservation of energy, to calculate the forces and velocities involved in a roller coaster's rotational motion. They take into account factors such as the mass and speed of the cars, the shape and size of the track, and frictional forces to determine the maximum and minimum speeds and forces experienced by the riders.

5. What safety measures are in place to ensure the safety of riders in a roller coaster's rotational motion?

Roller coasters undergo rigorous safety inspections and testing before they are opened to the public. The track, cars, and safety restraints are designed and constructed to withstand the forces involved in rotational motion. Additionally, roller coasters have multiple safety systems, such as sensors and emergency brakes, to prevent accidents and ensure the safety of riders.

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